%I #9 Aug 04 2023 15:47:37
%S 4,8,112,2720,103552,5764352,445521664,45890802176,6094567045120,
%T 1015769696055296,207796011483160576,51221187819965530112,
%U 14979210670593626472448,5128843038563324804464640,2032875137444937697755332608,923598907664745712876929548288
%N Coefficient (times -1) of the 1/r^(2n) term in the radial far-field expansion of the squared amplitude of a doubly-charged topological point defect (-2 or +2 vortex) in the two-dimensional Ginzburg-Landau equation.
%C Ginzburg-Landau vortex solutions are fundamental in the study of superconductors and superfluids.
%e a(3) = 112 because A(r)^2 = 1- 4/r^2 - 8/r^4 - 112/r^6 - ...
%t n = 17;
%t v = 2;
%t sol = AsymptoticDSolveValue[{4 z^3 f''[z] + 4 z^2 f'[z] - f[z] v^2 z + (1 - f[z]^2) f[z] == 0, f[0] == 1}, f[z], {z, 0, n}];
%t Rest@CoefficientList[1 - sol^2 + O[z]^n, z] (* _Andrey Zabolotskiy_, Aug 04 2023 *)
%Y Cf. A110818.
%K nonn
%O 1,1
%A _Greg Huber_, Oct 13 2005
%E Terms a(11) and beyond from _Andrey Zabolotskiy_, Aug 04 2023